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%I #17 May 04 2022 00:33:01
%S 1,2,3,4,5,6,7,8,9,10,112,12,135,14,15,16,175,18,192,20,21,224,2304,
%T 24,25,2625,27,28,294,30,315,32,336,343,35,36,375,384,392,40,4116,42,
%U 432,441,45,4608,4704,48,49,50,512,525,5376,54,55125,56,576,588,59049,60
%N Smallest 7-smooth number beginning with n.
%e a(23) = 2304 = 2^8*3^2 is the smallest 7-smooth number beginning with 23. (23, 230, 231, 232, ..., 239, 2301, 2302, 2303 etc. have a divisor > 10.)
%t a[n_] := Module[{d = IntegerDigits[n], k = 1}, While[Max[FactorInteger[k][[;; , 1]]] > 7 || Length[IntegerDigits[k]] < Length[d] || IntegerDigits[k][[1 ;; Length[d]]] != d, k++]; k]; Array[a, 60] (* _Amiram Eldar_, Apr 30 2022 *)
%o (PARI) hc(n) = local(f); f = factor(n); f[matsize(f)[1], 1] < 10;
%o a(n) = local(d, x); if (hc(n), return(n)); d = 1; while (d, for (i = 1, 10^d - 1, x = n*10^d + i; if (hc(x), return(x))); d++); \\ _David Wasserman_, Feb 11 2005
%Y Cf. A002473.
%K base,nonn
%O 0,2
%A _Amarnath Murthy_, Jul 09 2003
%E Corrected and extended by _David Wasserman_, Feb 11 2005
%E Name corrected by _J. Lowell_, Apr 30 2022
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